Does fees on Lightning network scale with transaction size?

Does fees on Lightning network scale with transaction size?

I did some reading around and various sources claim that the fee is proportional to the amount you would like to route. One source says that the fees are a flat fee + a certain percentage of your transaction amount.

Intuitively it makes sense that the fee should scale with the transaction size since a large transaction requires the intermediate routing nodes to temporarily 'freeze' up a larger amount in their channel, and/or creating a larger inbalance in their channels, which is of course not desirable.

So does anyone know exactly how fees scale with transaction size in the LN, or actually has equations to calculate it?

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